Does the fragmentation on the drive that your database’s data file is hosted on go with the database as it is backed up and restored elsewhere?
Assuming you are doing a file level backup then no it doesn't - how fragmented the file will be when it is copied/restored to another server will depend on the state of the file system there - if that server's disk is pretty full and the free space itself is fragmented (i.e. there are files all over the disk with gaps in between) and none of the gaps is big enough for the db file you are restoring then it will be fragmented on restore. If the disk is pretty clear it should restore to a single fragment.
If you are doing some form of disk (or block) level backup them it will because the copy is an image of the source so takes with it the layout of files on the disk.
If you are talking about a SAN it gets (potentially) a whole lot hazier as the SAN spreads it's data over loads of disks and depending on SAN make/model/feature set may do all sorts of things like auto optimising most used data to fastest devices etc. etc.